Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x-2y &= -8 \\ -x+9y &= 2\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-x = -9y+2$ Divide both sides by $-1$ to isolate $x$ $x = {9y - 2}$ Substitute this expression for $x$ in the first equation. $4({9y - 2}) - 2y = -8$ $36y - 8 - 2y = -8$ Simplify by combining terms, then solve for $y$ $34y - 8 = -8$ $34y = 0$ $y = 0$ Substitute $0$ for $y$ in the top equation. $4x-2( 0) = -8$ $4x = -8$ $4x = -8$ $x = -2$ The solution is $\enspace x = -2, \enspace y = 0$.